Inverse Heat Flux Problem in Quenching

2000 ◽  
Author(s):  
M. Khairul Alam ◽  
Rex J. Kuriger ◽  
Rong Zhong
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Surface Heat Flux ◽  
Measurement Errors ◽  
Heat Conduction Problem ◽  
Temperature Data ◽  
Surface Heat ◽  
Measured Temperature ◽  
Inverse Heat Conduction ◽  
Quenching Process

Abstract The quenching process is an important heat treatment method used to improve material properties. However, the heat transfer during quenching is particularly difficult to analyze and predict. To collect temperature data, quench probes have been used in controlled quenching experiments. The process of determination of the heat flux at the surface from the measured temperature data is the Inverse Heat Conduction Problem (IHCP), which is extremely sensitive to measurement errors. This paper reports on an experimental and theoretical study of quenching which is carried out to determine the surface heat flux history during a quenching process by an IHCP algorithm. The inverse heat conduction algorithm is applied to experimental data from a quenching experiment. The surface heat flux is then calculated, and the theoretical curve is compared with experimental results.

scholarly journals Analysis of One Dimensional Inverse Heat Conduction Problem : A Review

2012 ◽  
pp. 126-131
Author(s):  
Rakesh Kumar ◽  
Jayesh. P ◽  
Niranjan Sahoo
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Temperature Change ◽  
Surface Heat Flux ◽  
Working Condition ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Surface Heat ◽  
Inverse Heat Conduction ◽  
One Dimensional

A procedure to solve inverse heat conduction problem (IHCP) is to derive surface heat flux and temperature from temperature change inside a solid. The method proves to be very useful and powerful when a direct measurement of surface heat flux and temperature is difficult, owing to several working condition. The literature reviewed here discussion one dimensional inverse heat conduction problem. Procedure, criteria, methods and important results of other investigation are briefly discussed.

scholarly journals Application of the Finite Element Method to the Nonlinear Inverse Heat Conduction Problem Using Beck’s Second Method

1980 ◽  
Vol 102 (2) ◽  
pp. 168-176 ◽  
Author(s):  
B. R. Bass
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Finite Element ◽  
Heat Conduction ◽  
Interior Point ◽  
Surface Heat Flux ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Surface Heat ◽  
Inverse Heat Conduction

The calculation of the surface temperature and surface heat flux from a measured temperature history at an interior point of a body is identified in the literature as the inverse heat conduction problem. This paper presents, to the author’s knowledge, the first application of a solution technique for the inverse problem that utilizes a finite element heat conduction model and Beck’s nonlinear estimation procedure. The technique is applicable to the one-dimensional nonlinear model with temperature-dependent thermophysical properties. The formulation is applied first to a numerical example with a known solution. The example treated is that of a periodic heat flux imposed on the surface of a rod. The computed surface heat flux is compared with the imposed heat flux to evaluate the performance of the technique in solving the inverse problem. Finally, the technique is applied to an experimentally determined temperature transient taken from an interior point of an electrically-heated composite rod. The results are compared with those obtained by applying a finite difference inverse technique to the same data.

Finite Element Formulation for Two-Dimensional Inverse Heat Conduction Analysis

1992 ◽  
Vol 114 (3) ◽  
pp. 553-557 ◽  
Author(s):  
T. R. Hsu ◽  
N. S. Sun ◽  
G. G. Chen ◽  
Z. L. Gong
Keyword(s):  
Heat Flux ◽  
Finite Element ◽  
Heat Conduction ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Element Formulation ◽  
Two Dimensional ◽  
Inverse Heat Conduction ◽  
Discrete Point ◽  
Element Algorithm

This paper presents a finite element algorithm for two-dimensional nonlinear inverse heat conduction analysis. The proposed method is capable of handling both unknown surface heat flux and unknown surface temperature of solids using temperature histories measured at a few discrete point. The proposed algorithms were used in the study of the thermofracture behavior of leaking pipelines with experimental verifications.

A Near Real-Time Solution Approach for Surface Heat Flux Estimation in One Dimensional Inverse Heat Conduction Problems With Moving Boundary

2019 ◽  
Author(s):  
Obinna Uyanna ◽  
Hamidreza Najafi
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Real Time ◽  
Surface Heat Flux ◽  
Moving Boundary ◽  
Surface Heat ◽  
Inverse Heat Conduction ◽  
Heat Flux Estimation ◽  
Flux Estimation ◽  
Inverse Heat Conduction Problems

Abstract Developing accurate and efficient solutions for inverse heat conduction problems allows advancements in the heat flux measurement techniques for many applications. In the present paper, a one-dimensional medium with a moving boundary is considered. It is assumed that two thermocouples are used to measure temperature at two locations within the medium while the front boundary is moving towards the back surface. Determining surface heat flux using measured temperature data is an inverse heat conduction problem. A filter based Tikhonov regularization method is used to develop a solution for this problem. Filter coefficients are calculated for various thicknesses of the medium. It is demonstrated that the filter coefficients can be interpolated to calculate the appropriate values for each thickness while it is continuously moving at a known rate. The use of filter method allows near real-time heat flux estimation. The developed solution is validated through several numerical test cases including a test case for a moving boundary in a medium modeled in COMSOL. It is shown that the proposed solution can effectively estimate the surface heat flux on the moving boundary in a near real-time fashion.

Determination of Surface Heat Flux in Quenching

1999 ◽  
Author(s):  
M. K. Alam ◽  
H. Pasic ◽  
K. Anagurthi ◽  
R. Zhong
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Analytical Solution ◽  
Surface Heat Flux ◽  
Measurement Errors ◽  
Numerical Solutions ◽  
Heat Conduction Problem ◽  
Initial Guess ◽  
Surface Heat

Abstract Quench probes have been used to collect temperature data in controlled quenching experiments; the data is then used to deduce the heat transfer coefficients in the quenching medium. The process of determination of the heat transfer coefficient at the surface is the inverse heat conduction problem, which is extremely sensitive to measurement errors. This paper reports on an experimental and theoretical study of quenching carried out to determine the surface heat flux history during a quenching process by an inverse algorithm based on an analytical solution. The algorithm is applied to experimental data from a quenching experiment. The surface heat flux is then calculated, and the theoretical curve obtained from the analytical solution is compared with experimental results. The inverse calculation appears to produce fast, stable, but approximate results. These results can be used as the initial guess to improve the efficiency of iterative numerical solutions which are sensitive to the initial guess.

Methodology for Comparison of Inverse Heat Conduction Methods

1988 ◽  
Vol 110 (1) ◽  
pp. 30-37 ◽  
Author(s):  
M. Raynaud ◽  
J. V. Beck
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Standard Deviation ◽  
Measurement Errors ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Inverse Methods ◽  
Test Problems ◽  
Test Case ◽  
Inverse Heat Conduction

The inverse heat conduction problem involves the calculation of the surface heat flux from transient measured temperatures inside solids. The deviation of the estimated heat flux from the true heat flux due to stabilization procedures is called the deterministic bias. This paper defines two test problems that show the tradeoff between deterministic bias and sensitivity to measurement errors of inverse methods. For a linear problem, with the statistical assumptions of additive and uncorrelated errors having constant variance and zero mean, the second test case gives the standard deviation of the estimated heat flux. A methodology for the quantitative comparison of deterministic bias and standard deviation of inverse methods is proposed. Four numerical inverse methods are compared.

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